Nobody is lying, the redacted agreements do indeed show that the UK agreement is dated to a day after the EU agreement but that says nothing about when money changed hands or prior deals or commitments. You get a 3 month difference between the UK and the EU because the UK had an agreement with AstraZeneca all the way back on the 17th of May (note: June -> Aug is not 3 months, that's sloppy reporting from your linked website) as can be seen here: https://www.gov.uk/government/news/funding-and-manufacturing...

or here: https://www.theguardian.com/society/2020/may/17/uk-plans-38m...

and this is on top of funding Oxford had received from the UK prior to the Oxford-AZ deal. https://www.ox.ac.uk/news/2020-03-24-oxfords-covid-19-resear...

Yet the publicly announced deal with the EU was on the 27th of August: https://www.euractiv.com/section/coronavirus/news/eu-pays-e3...

It should be noted at this point that France, Germany, Italy, and the Netherlands, had jointly negotiated a deal with AZ in June but my understanding is that after an EU27 vote the EC took over negotiations and you get the final (and first for the EU) deal in August.

Why the redacted UK agreement is dated 28th of August is anybodies guess but some things should be made clear, firstly that the UK started funding AZ in May and not late August, secondly that they did this a month before other EU countries had reached an agreement with AZ, and finally that the EC getting involved added a further 2 months to the negotiation.